def test_shape(self): # try to avoid introspector picking up this model Gen2D = copy.deepcopy(models.Generic2dOscillator) class CouplingShapeTestModel(Gen2D): def __init__(self, test_case=None, n_node=None, **kwds): super(CouplingShapeTestModel, self).__init__(**kwds) self.cvar = numpy.r_[0, 1] self.n_node = n_node self.test_case = test_case def dfun(self, state, coupling, local_coupling): if self.test_case is not None: self.test_case.assert_equal((2, self.n_node, 1), coupling.shape) return state surf = cortex.Cortex(region_mapping_data=region_mapping.RegionMapping( load_file="regionMapping_16k_76.txt"), load_file="cortex_16384.zip") sim = simulator.Simulator(model=CouplingShapeTestModel( self, surf.vertices.shape[0]), connectivity=connectivity.Connectivity( load_file="connectivity_76.zip"), surface=surf) sim.configure() for _ in sim(simulation_length=sim.integrator.dt * 2): pass
class Simulator(core.Type): "A Simulator assembles components required to perform simulations." connectivity = connectivity.Connectivity( label="Long-range connectivity", default=None, order=1, required=True, filters_ui=[ UIFilter(linked_elem_name="region_mapping_data", linked_elem_field=FilterChain.datatype + "._connectivity", linked_elem_parent_name="surface", linked_elem_parent_option=None), UIFilter(linked_elem_name="region_mapping", linked_elem_field=FilterChain.datatype + "._connectivity", linked_elem_parent_name="monitors", linked_elem_parent_option="EEG"), UIFilter(linked_elem_name="region_mapping", linked_elem_field=FilterChain.datatype + "._connectivity", linked_elem_parent_name="monitors", linked_elem_parent_option="MEG"), UIFilter(linked_elem_name="region_mapping", linked_elem_field=FilterChain.datatype + "._connectivity", linked_elem_parent_name="monitors", linked_elem_parent_option="iEEG") ], doc="""A tvb.datatypes.Connectivity object which contains the structural long-range connectivity data (i.e., white-matter tracts). In combination with the ``Long-range coupling function`` it defines the inter-regional connections. These couplings undergo a time delay via signal propagation with a propagation speed of ``Conduction Speed``""") conduction_speed = basic.Float( label="Conduction Speed", default=3.0, order=2, required=False, range=basic.Range(lo=0.01, hi=100.0, step=1.0), doc="""Conduction speed for ``Long-range connectivity`` (mm/ms)""") coupling = coupling.Coupling( label="Long-range coupling function", default=coupling.Linear(), required=True, order=2, doc="""The coupling function is applied to the activity propagated between regions by the ``Long-range connectivity`` before it enters the local dynamic equations of the Model. Its primary purpose is to 'rescale' the incoming activity to a level appropriate to Model.""") surface = cortex.Cortex( label="Cortical surface", default=None, order=3, required=False, filters_backend=FilterChain( fields=[FilterChain.datatype + '._valid_for_simulations'], operations=["=="], values=[True]), filters_ui=[ UIFilter(linked_elem_name="projection_matrix_data", linked_elem_field=FilterChain.datatype + "._sources", linked_elem_parent_name="monitors", linked_elem_parent_option="EEG"), UIFilter(linked_elem_name="local_connectivity", linked_elem_field=FilterChain.datatype + "._surface", linked_elem_parent_name="surface", linked_elem_parent_option=None) ], doc="""By default, a Cortex object which represents the cortical surface defined by points in the 3D physical space and their neighborhood relationship. In the current TVB version, when setting up a surface-based simulation, the option to configure the spatial spread of the ``Local Connectivity`` is available.""") stimulus = patterns.SpatioTemporalPattern( label="Spatiotemporal stimulus", default=None, order=4, required=False, doc= """A ``Spatiotemporal stimulus`` can be defined at the region or surface level. It's composed of spatial and temporal components. For region defined stimuli the spatial component is just the strength with which the temporal component is applied to each region. For surface defined stimuli, a (spatial) function, with finite-support, is used to define the strength of the stimuli on the surface centred around one or more focal points. In the current version of TVB, stimuli are applied to the first state variable of the ``Local dynamic model``.""") model = models.Model( label="Local dynamic model", default=models.Generic2dOscillator, required=True, order=5, doc="""A tvb.simulator.Model object which describe the local dynamic equations, their parameters, and, to some extent, where connectivity (local and long-range) enters and which state-variables the Monitors monitor. By default the 'Generic2dOscillator' model is used. Read the Scientific documentation to learn more about this model.""") integrator = integrators.Integrator( label="Integration scheme", default=integrators.HeunDeterministic, required=True, order=6, doc="""A tvb.simulator.Integrator object which is an integration scheme with supporting attributes such as integration step size and noise specification for stochastic methods. It is used to compute the time courses of the model state variables.""") initial_conditions = arrays.FloatArray( label="Initial Conditions", default=None, order=-1, required=False, doc="""Initial conditions from which the simulation will begin. By default, random initial conditions are provided. Needs to be the same shape as simulator 'history', ie, initial history function which defines the minimal initial state of the network with time delays before time t=0. If the number of time points in the provided array is insufficient the array will be padded with random values based on the 'state_variables_range' attribute.""") monitors = monitors.Monitor( label="Monitor(s)", default=monitors.TemporalAverage, required=True, order=8, select_multiple=True, doc="""A tvb.simulator.Monitor or a list of tvb.simulator.Monitor objects that 'know' how to record relevant data from the simulation. Two main types exist: 1) simple, spatial and temporal, reductions (subsets or averages); 2) physiological measurements, such as EEG, MEG and fMRI. By default the Model's specified variables_of_interest are returned, temporally downsampled from the raw integration rate to a sample rate of 1024Hz.""") simulation_length = basic.Float( label="Simulation Length (ms, s, m, h)", default=1000.0, # ie 1 second required=True, order=9, doc="""The length of a simulation (default in milliseconds).""") history = None # type: SparseHistory @property def good_history_shape(self): "Returns expected history shape." n_reg = self.connectivity.number_of_regions shape = self.horizon, len( self.model.state_variables), n_reg, self.model.number_of_modes return shape calls = 0 current_step = 0 number_of_nodes = None _memory_requirement_guess = None _memory_requirement_census = None _storage_requirement = None _runtime = None # methods consist of # 1) generic configure # 2) component specific configure # 3) loop preparation # 4) loop step # 5) estimations def preconfigure(self): "Configure just the basic fields, so that memory can be estimated." self.connectivity.configure() if self.surface: self.surface.configure() if self.stimulus: self.stimulus.configure() self.coupling.configure() self.model.configure() self.integrator.configure() # monitors needs to be a list or tuple, even if there is only one... if not isinstance(self.monitors, (list, tuple)): self.monitors = [self.monitors] # Configure monitors for monitor in self.monitors: monitor.configure() # "Nodes" refers to either regions or vertices + non-cortical regions. if self.surface is None: self.number_of_nodes = self.connectivity.number_of_regions LOG.info('Region simulation with %d ROI nodes', self.number_of_nodes) else: rm = self.surface.region_mapping unmapped = self.connectivity.unmapped_indices(rm) self._regmap = numpy.r_[rm, unmapped] self.number_of_nodes = self._regmap.shape[0] LOG.info( 'Surface simulation with %d vertices + %d non-cortical, %d total nodes', rm.size, unmapped.size, self.number_of_nodes) self._guesstimate_memory_requirement() def configure(self, full_configure=True): """Configure simulator and its components. The first step of configuration is to run the configure methods of all the Simulator's components, ie its traited attributes. Configuration of a Simulator primarily consists of calculating the attributes, etc, which depend on the combinations of the Simulator's traited attributes (keyword args). Converts delays from physical time units into integration steps and updates attributes that depend on combinations of the 6 inputs. Returns ------- sim: Simulator The configured Simulator instance. """ if full_configure: # When run from GUI, preconfigure is run separately, and we want to avoid running that part twice self.preconfigure() # Make sure spatialised model parameters have the right shape (number_of_nodes, 1) excluded_params = ("state_variable_range", "variables_of_interest", "noise", "psi_table", "nerf_table") spatial_reshape = self.model.spatial_param_reshape for param in self.model.trait.keys(): if param in excluded_params: continue # If it's a surface sim and model parameters were provided at the region level region_parameters = getattr(self.model, param) if self.surface is not None: if region_parameters.size == self.connectivity.number_of_regions: new_parameters = region_parameters[ self.surface.region_mapping].reshape(spatial_reshape) setattr(self.model, param, new_parameters) region_parameters = getattr(self.model, param) if region_parameters.size == self.number_of_nodes: new_parameters = region_parameters.reshape(spatial_reshape) setattr(self.model, param, new_parameters) # Configure spatial component of any stimuli self._configure_stimuli() # Set delays, provided in physical units, in integration steps. self.connectivity.set_idelays(self.integrator.dt) self.horizon = self.connectivity.idelays.max() + 1 # Reshape integrator.noise.nsig, if necessary. if isinstance(self.integrator, integrators.IntegratorStochastic): self._configure_integrator_noise() # Setup history self._configure_history(self.initial_conditions) # Configure Monitors to work with selected Model, etc... self._configure_monitors() # Estimate of memory usage. self._census_memory_requirement() # Allow user to chain configure to another call or assignment. return self def _handle_random_state(self, random_state): if random_state is not None: if isinstance(self.integrator, integrators.IntegratorStochastic): self.integrator.noise.random_stream.set_state(random_state) msg = "random_state supplied with seed %s" LOG.info(msg, self.integrator.noise.random_stream.get_state()[1][0]) else: LOG.warn( "random_state supplied for non-stochastic integration") def _prepare_local_coupling(self): if self.surface is None: local_coupling = 0.0 else: if self.surface.coupling_strength.size == 1: local_coupling = (self.surface.coupling_strength[0] * self.surface.local_connectivity.matrix) elif self.surface.coupling_strength.size == self.surface.number_of_vertices: ind = numpy.arange(self.number_of_nodes, dtype=numpy.intc) vec_cs = numpy.zeros((self.number_of_nodes, )) vec_cs[:self.surface. number_of_vertices] = self.surface.coupling_strength sp_cs = scipy.sparse.csc_matrix( (vec_cs, (ind, ind)), shape=(self.number_of_nodes, self.number_of_nodes)) local_coupling = sp_cs * self.surface.local_connectivity.matrix if local_coupling.shape[1] < self.number_of_nodes: # must match unmapped indices handling in preconfigure from scipy.sparse import csr_matrix, vstack, hstack nn = self.number_of_nodes npad = nn - local_coupling.shape[0] rpad = csr_matrix((local_coupling.shape[0], npad)) bpad = csr_matrix((npad, nn)) local_coupling = vstack([hstack([local_coupling, rpad]), bpad]) return local_coupling def _prepare_stimulus(self): if self.stimulus is None: stimulus = 0.0 else: time = numpy.r_[0.0:self.simulation_length:self.integrator.dt] self.stimulus.configure_time(time.reshape((1, -1))) stimulus = numpy.zeros((self.model.nvar, self.number_of_nodes, 1)) LOG.debug("stimulus shape is: %s", stimulus.shape) return stimulus def _loop_compute_node_coupling(self, step): "Compute delayed node coupling values." coupling = self.coupling(step, self.history) if self.surface is not None: coupling = coupling[:, self._regmap] return coupling def _loop_update_stimulus(self, step, stimulus): "Update stimulus values for current time step." if self.stimulus is not None: # TODO stim_step != current step stim_step = step - (self.current_step + 1) stimulus[self.model.cvar, :, :] = self.stimulus(stim_step).reshape( (1, -1, 1)) def _loop_update_history(self, step, n_reg, state): "Update history." if self.surface is not None and state.shape[ 1] > self.connectivity.number_of_regions: region_state = numpy.zeros( (n_reg, state.shape[0], state.shape[2])) # temp (node, cvar, mode) numpy_add_at(region_state, self._regmap, state.transpose( (1, 0, 2))) # sum within region region_state /= numpy.bincount(self._regmap).reshape( (-1, 1, 1)) # div by n node in region state = region_state.transpose((1, 0, 2)) # (cvar, node, mode) self.history.update(step, state) def _loop_monitor_output(self, step, state): observed = self.model.observe(state) output = [monitor.record(step, observed) for monitor in self.monitors] if any(outputi is not None for outputi in output): return output def __call__(self, simulation_length=None, random_state=None): """ Return an iterator which steps through simulation time, generating monitor outputs. See the run method for a convenient way to collect all output in one call. :param simulation_length: Length of the simulation to perform in ms. :param random_state: State of NumPy RNG to use for stochastic integration. :return: Iterator over monitor outputs. """ self.calls += 1 if simulation_length is not None: self.simulation_length = simulation_length # intialization self._guesstimate_runtime() self._calculate_storage_requirement() self._handle_random_state(random_state) n_reg = self.connectivity.number_of_regions local_coupling = self._prepare_local_coupling() stimulus = self._prepare_stimulus() state = self.current_state # integration loop n_steps = int(math.ceil(self.simulation_length / self.integrator.dt)) for step in range(self.current_step + 1, self.current_step + n_steps + 1): # needs implementing by hsitory + coupling? node_coupling = self._loop_compute_node_coupling(step) self._loop_update_stimulus(step, stimulus) state = self.integrator.scheme(state, self.model.dfun, node_coupling, local_coupling, stimulus) self._loop_update_history(step, n_reg, state) output = self._loop_monitor_output(step, state) if output is not None: yield output self.current_state = state self.current_step = self.current_step + n_steps - 1 # -1 : don't repeat last point def _configure_history(self, initial_conditions): """ Set initial conditions for the simulation using either the provided initial_conditions or, if none are provided, the model's initial() method. This method is called durin the Simulator's __init__(). Any initial_conditions that are provided as an argument are expected to have dimensions 1, 2, and 3 with shapse corresponding to the number of state_variables, nodes and modes, respectively. If the provided inital_conditions are shorter in time (dim=0) than the required history the model's initial() method is called to make up the difference. """ rng = numpy.random if hasattr(self.integrator, 'noise'): rng = self.integrator.noise.random_stream # Default initial conditions if initial_conditions is None: n_time, n_svar, n_node, n_mode = self.good_history_shape LOG.info( 'Preparing initial history of shape %r using model.initial()', self.good_history_shape) if self.surface is not None: n_node = self.number_of_nodes history = self.model.initial(self.integrator.dt, (n_time, n_svar, n_node, n_mode), rng) # ICs provided else: # history should be [timepoints, state_variables, nodes, modes] LOG.info('Using provided initial history of shape %r', initial_conditions.shape) n_time, n_svar, n_node, n_mode = ic_shape = initial_conditions.shape nr = self.connectivity.number_of_regions if self.surface is not None and n_node == nr: initial_conditions = initial_conditions[:, :, self._regmap] return self._configure_history(initial_conditions) elif ic_shape[1:] != self.good_history_shape[1:]: raise ValueError( "Incorrect history sample shape %s, expected %s" % ic_shape[1:], self.good_history_shape[1:]) else: if ic_shape[0] >= self.horizon: LOG.debug("Using last %d time-steps for history.", self.horizon) history = initial_conditions[ -self.horizon:, :, :, :].copy() else: LOG.debug('Padding initial conditions with model.initial') history = self.model.initial(self.integrator.dt, self.good_history_shape, rng) shift = self.current_step % self.horizon history = numpy.roll(history, -shift, axis=0) history[:ic_shape[0], :, :, :] = initial_conditions history = numpy.roll(history, shift, axis=0) self.current_step += ic_shape[0] - 1 LOG.info('Final initial history shape is %r', history.shape) # create initial state from history self.current_state = history[self.current_step % self.horizon].copy() LOG.debug('initial state has shape %r' % (self.current_state.shape, )) if self.surface is not None and history.shape[ 2] > self.connectivity.number_of_regions: n_reg = self.connectivity.number_of_regions (nt, ns, _, nm), ax = history.shape, (2, 0, 1, 3) region_history = numpy.zeros((nt, ns, n_reg, nm)) numpy_add_at(region_history.transpose(ax), self._regmap, history.transpose(ax)) region_history /= numpy.bincount(self._regmap).reshape((-1, 1)) history = region_history # create history query implementation self.history = SparseHistory(self.connectivity.weights, self.connectivity.idelays, self.model.cvar, self.model.number_of_modes) # initialize its buffer self.history.initialize(history) def _configure_integrator_noise(self): """ This enables having noise to be state variable specific and/or to enter only via specific brain structures, for example it we only want to consider noise as an external input entering the brain via appropriate thalamic nuclei. Support 3 possible shapes: 1) number_of_nodes; 2) number_of_state_variables; and 3) (number_of_state_variables, number_of_nodes). """ noise = self.integrator.noise if self.integrator.noise.ntau > 0.0: self.integrator.noise.configure_coloured( self.integrator.dt, self.good_history_shape[1:]) else: self.integrator.noise.configure_white(self.integrator.dt, self.good_history_shape[1:]) if self.surface is not None: if self.integrator.noise.nsig.size == self.connectivity.number_of_regions: self.integrator.noise.nsig = self.integrator.noise.nsig[ self.surface.region_mapping] elif self.integrator.noise.nsig.size == self.model.nvar * self.connectivity.number_of_regions: self.integrator.noise.nsig = self.integrator.noise.nsig[:, self. surface . region_mapping] good_nsig_shape = (self.model.nvar, self.number_of_nodes, self.model.number_of_modes) nsig = self.integrator.noise.nsig LOG.debug("Given noise shape is %s", nsig.shape) if nsig.shape in (good_nsig_shape, (1, )): return elif nsig.shape == (self.model.nvar, ): nsig = nsig.reshape((self.model.nvar, 1, 1)) elif nsig.shape == (self.number_of_nodes, ): nsig = nsig.reshape((1, self.number_of_nodes, 1)) elif nsig.shape == (self.model.nvar, self.number_of_nodes): nsig = nsig.reshape((self.model.nvar, self.number_of_nodes, 1)) else: msg = "Bad Simulator.integrator.noise.nsig shape: %s" LOG.error(msg % str(nsig.shape)) LOG.debug("Corrected noise shape is %s", nsig.shape) self.integrator.noise.nsig = nsig def _configure_monitors(self): """ Configure the requested Monitors for this Simulator """ # Coerce to list if required if not isinstance(self.monitors, (list, tuple)): self.monitors = [self.monitors] # Configure monitors for monitor in self.monitors: monitor.config_for_sim(self) def _configure_stimuli(self): """ Configure the defined Stimuli for this Simulator """ if self.stimulus is not None: if self.surface: self.stimulus.configure_space(self.surface.region_mapping) else: self.stimulus.configure_space() # used by simulator adaptor def memory_requirement(self): """ Return an estimated of the memory requirements (Bytes) for this simulator's current configuration. """ self._guesstimate_memory_requirement() return self._memory_requirement_guess # appears to be unused def runtime(self, simulation_length): """ Return an estimated run time (seconds) for the simulator's current configuration and a specified simulation length. """ self.simulation_length = simulation_length self._guesstimate_runtime() return self._runtime # used by simulator adaptor def storage_requirement(self, simulation_length): """ Return an estimated storage requirement (Bytes) for the simulator's current configuration and a specified simulation length. """ self.simulation_length = simulation_length self._calculate_storage_requirement() return self._storage_requirement def _guesstimate_memory_requirement(self): """ guesstimate the memory required for this simulator. Guesstimate is based on the shape of the dominant arrays, and as such can operate before configuration. NOTE: Assumes returned/yeilded data is in some sense "taken care of" in the world outside the simulator, and so doesn't consider it, making the simulator's history, and surface if present, the dominant memory pigs... """ if self.surface: number_of_nodes = self.surface.number_of_vertices else: number_of_nodes = self.connectivity.number_of_regions number_of_regions = self.connectivity.number_of_regions magic_number = 2.42 # Current guesstimate is low by about a factor of 2, seems safer to over estimate... bits_64 = 8.0 # Bytes bits_32 = 4.0 # Bytes #NOTE: The speed hack for getting the first element of hist shape should # partially resolves calling of this method with a non-configured # connectivity, there remains the less common issue if no tract_lengths... hist_shape = ( self.connectivity.tract_lengths.max() / (self.conduction_speed or self.connectivity.speed or 3.0) / self.integrator.dt, self.model.nvar, number_of_nodes, self.model.number_of_modes) LOG.debug("Estimated history shape is %r", hist_shape) memreq = numpy.prod(hist_shape) * bits_64 if self.surface: memreq += self.surface.number_of_triangles * 3 * bits_32 * 2 # normals memreq += self.surface.number_of_vertices * 3 * bits_64 * 2 # normals memreq += number_of_nodes * number_of_regions * bits_64 * 4 # region_mapping, region_average, region_sum #???memreq += self.surface.local_connectivity.matrix.nnz * 8 if not hasattr(self.monitors, '__len__'): self.monitors = [self.monitors] for monitor in self.monitors: if not isinstance(monitor, monitors.Bold): stock_shape = (monitor.period / self.integrator.dt, self.model.variables_of_interest.shape[0], number_of_nodes, self.model.number_of_modes) memreq += numpy.prod(stock_shape) * bits_64 if hasattr(monitor, "sensors"): try: memreq += number_of_nodes * monitor.sensors.number_of_sensors * bits_64 # projection_matrix except AttributeError: LOG.debug( "No sensors specified, guessing memory based on default EEG." ) memreq += number_of_nodes * 62.0 * bits_64 else: stock_shape = (monitor.hrf_length * monitor._stock_sample_rate, self.model.variables_of_interest.shape[0], number_of_nodes, self.model.number_of_modes) interim_stock_shape = ( 1.0 / (2.0**-2 * self.integrator.dt), self.model.variables_of_interest.shape[0], number_of_nodes, self.model.number_of_modes) memreq += numpy.prod(stock_shape) * bits_64 memreq += numpy.prod(interim_stock_shape) * bits_64 if psutil and memreq > psutil.virtual_memory().total: LOG.warning( "There may be insufficient memory for this simulation.") self._memory_requirement_guess = magic_number * memreq msg = "Memory requirement estimate: simulation will need about %.1f MB" LOG.info(msg, self._memory_requirement_guess / 2**20) def _census_memory_requirement(self): """ Guesstimate the memory required for this simulator. Guesstimate is based on a census of the dominant arrays after the simulator has been configured. NOTE: Assumes returned/yeilded data is in some sense "taken care of" in the world outside the simulator, and so doesn't consider it, making the simulator's history, and surface if present, the dominant memory pigs... """ magic_number = 2.42 # Current guesstimate is low by about a factor of 2, seems safer to over estimate... memreq = self.history.nbytes try: memreq += self.surface.triangles.nbytes * 2 memreq += self.surface.vertices.nbytes * 2 memreq += self.surface.region_mapping.nbytes * self.number_of_nodes * 8. * 4 # region_average, region_sum memreq += self.surface.eeg_projection.nbytes memreq += self.surface.local_connectivity.matrix.nnz * 8 except AttributeError: pass for monitor in self.monitors: memreq += monitor._stock.nbytes if isinstance(monitor, monitors.Bold): memreq += monitor._interim_stock.nbytes if psutil and memreq > psutil.virtual_memory().total: LOG.warning("Memory estimate exceeds total available RAM.") self._memory_requirement_census = magic_number * memreq #import pdb; pdb.set_trace() msg = "Memory requirement census: simulation will need about %.1f MB" LOG.info(msg % (self._memory_requirement_census / 1048576.0)) def _guesstimate_runtime(self): """ Estimate the runtime for this simulator. Spread in parallel executions of larger arrays means this will be an over-estimation, or rather a single threaded estimation... Different choice of integrators and monitors has an additional effect, on the magic number though relatively minor """ magic_number = 6.57e-06 # seconds self._runtime = (magic_number * self.number_of_nodes * self.model.nvar * self.model.number_of_modes * self.simulation_length / self.integrator.dt) msg = "Simulation runtime should be about %0.3f seconds" LOG.info(msg, self._runtime) def _calculate_storage_requirement(self): """ Calculate the storage requirement for the simulator, configured with models, monitors, etc being run for a particular simulation length. While this is only approximate, it is far more reliable/accurate than the memory and runtime guesstimates. """ LOG.info("Calculating storage requirement for ...") strgreq = 0 for monitor in self.monitors: # Avoid division by zero for monitor not yet configured # (in framework this is executed, when only preconfigure has been called): current_period = monitor.period or self.integrator.dt strgreq += (TvbProfile.current.MAGIC_NUMBER * self.simulation_length * self.number_of_nodes * self.model.nvar * self.model.number_of_modes / current_period) LOG.info("Calculated storage requirement for simulation: %d " % int(strgreq)) self._storage_requirement = int(strgreq) def run(self, **kwds): "Convenience method to call the simulator with **kwds and collect output data." ts, xs = [], [] for _ in self.monitors: ts.append([]) xs.append([]) wall_time_start = time.time() for data in self(**kwds): for tl, xl, t_x in zip(ts, xs, data): if t_x is not None: t, x = t_x tl.append(t) xl.append(x) elapsed_wall_time = time.time() - wall_time_start LOG.info("%.3f s elapsed, %.3fx real time", elapsed_wall_time, elapsed_wall_time * 1e3 / self.simulation_length) for i in range(len(ts)): ts[i] = numpy.array(ts[i]) xs[i] = numpy.array(xs[i]) return list(zip(ts, xs))